Dependent types and Program Equivalence

Simple item page
dc.contributor.authorJia, Limin
dc.contributor.authorZhao, Jianzhou
dc.contributor.authorSjoberg, Vilhelm
dc.contributor.authorWeirich, Stephanie
dc.date2023-05-17T07:13:21.000
dc.date.accessioned2023-05-22T12:50:03Z
dc.date.available2023-05-22T12:50:03Z
dc.date.issued2010-01-17
dc.date.submitted2012-07-23T12:38:32-07:00
dc.description.abstractThe definition of type equivalence is one of the most important design issues for any typed language. In dependently-typed languages, because terms appear in types, this definition must rely on a definition of term equivalence. In that case, decidability of type checking requires decidability for the term equivalence relation. Almost all dependently-typed languages require this relation to be decidable. Some, such as Coq, Epigram or Agda, do so by employing analyses to force all programs to terminate. Conversely, others, such as DML, ATS, Omega, or Haskell, allow nonterminating computation, but do not allow those terms to appear in types. Instead, they identify a terminating index language and use singleton types to connect indices to computation. In both cases, decidable type checking comes at a cost, in terms of complexity and expressiveness. Conversely, the benefits to be gained by decidable type checking are modest. Termination analyses allow dependently typed programs to verify total correctness properties. However, decidable type checking is not a prerequisite for type safety. Furthermore, decidability does not imply tractability. A decidable approximation of program equivalence may not be useful in practice. Therefore, we take a different approach: instead of a fixed notion for term equi valence, we parameterize our type system with an abstract relation that is not n ecessarily decidable. We then design a novel set of typing rules that require on ly weak properties of this abstract relation in the proof of the preservation an d progress lemmas. This design provides flexibility: we compare valid instantiat ions of term equivalence which range from beta-equivalence, to contextual equiva lence, to some exotic equivalences.
dc.description.comments© ACM, 2010. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in 37th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, {(2010)} http://dx.doi.org/10.1145/1707801.1706333= Email permissions@acm.org
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/6698
dc.legacy.articleid1668
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1668&context=cis_papers&unstamped=1
dc.source.issue632
dc.source.journalDepartmental Papers (CIS)
dc.source.statuspublished
dc.subject.otherComputer Sciences
dc.titleDependent types and Program Equivalence
dc.typePresentation
digcom.contributor.authorJia, Limin
digcom.contributor.authorZhao, Jianzhou
digcom.contributor.authorSjoberg, Vilhelm
digcom.contributor.authorisAuthorOfPublication|email:sweirich@cis.upenn.edu|institution:University of Pennsylvania|Weirich, Stephanie
digcom.identifiercis_papers/632
digcom.identifier.contextkey3121930
digcom.identifier.submissionpathcis_papers/632
digcom.typeconference
dspace.entity.typePublication
relation.isAuthorOfPublicationb66c11a3-4446-4985-a8af-67bf0f02b419
relation.isAuthorOfPublicationb66c11a3-4446-4985-a8af-67bf0f02b419
relation.isAuthorOfPublication.latestForDiscoveryb66c11a3-4446-4985-a8af-67bf0f02b419
upenn.schoolDepartmentCenterDepartmental Papers (CIS)
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
popl10_lambda_eek.pdf
Size:
315.26 KB
Format:
Adobe Portable Document Format
Download
Collection
Presentations